SHIRASGAON, India—More than 500 low-caste Hindus filled the Veera Maidan, an open field at the edge of a dusty Maharashtra village, on a recent Sunday night. Neighbors openly gawked from porches as the throngs of people filed in, many dressed in symbolic white saris and kurtas. Under floodlights, they chanted: “I shall have no faith in Rama and Krishna who are believed to be incarnations of God nor shall I worship them. … I do not and shall not believe that Lord Buddha was the...